One of the most important measures to compare countries economically is **Gross Domestic Product** (GDP). This measure shows the market value of all goods and services produced by a country in a given period of time. Moreover, it is usually calculated on an **annual basis** and there are different ways of calculating it: nominal GDP, real GDP, GDP at PPP, nominal GDP per capita, etc.

Let’s focus on the **nominal GDP** since the rest of indexes are variations of it. The following equation express how it is calculated:

$$GDP = C + I +G +(X – M)$$

Where:

- C \(\equiv\) consumer spending
- I \(\equiv\) business investment
- G \(\equiv\) government spending
- (X-M) \(\equiv\) net exports

In addition, in order to find out the value of the **GDP per capita**, we would only have to divide the value of the GDP previously obtained by the number of the country’s inhabitants.

$$GDP \: per \: capita = \frac{GDP}{N}$$

However, is GDP a fair measure to compare countries at a macroeconomic level?

In order to answer this question, let’s talk about the **Penn effect**.

## What is the Penn effect?

The Penn effect states that whether the GDP is converted at market exchange rates, the economic distance between the most and least developed countries becomes more remarkable.

This is due to the fact that price levels in **high-income** countries are higher than in **low-income** countries. Furthermore, in order to compare the GDP levels of different countries, the evaluation needs to be in the same currency. So, when converting those values into a common currency, the exchange rate that has been applied does not take into account those price level differences.

One consequence of the Penn effect is the **Harrod Balassa Samuelson** (HBS) effect, which we have already discussed in previous posts.

### Harrod Balassa Samuelson effect

The HBS effect states that the prices in more developed countries will be higher than in less developed countries.

These differences should occur in **non-tradable goods** and not in tradable ones. But, the differences can be found in both types of goods

One example of a non-tradable service could be a hotel accommodation, whereas an example of a tradable service could be a financial service or software development.

If the **tradable goods sector’s** wages increase, the wages of the non-tradable sector will also increase. This will lead to higher prices in both sectors, which will result in higher inflation rates in countries that are growing fast.

This is because the **prices **of tradable goods will be the same in all countries. Therefore, as that price is not going to vary, the wages of the producers will depend on their productivity. Thus, more productive countries will have higher wages, which will be reflected in higher prices for non-tradable goods. This is due to, assuming that the productivity of non-tradable goods is similar, higher wages will lead to higher prices for non-tradable goods.

As a consequence, we can say that the differences that occur between the **Purchasing Power Parity** and the **currency exchange rates** are related to the differences in the production of tradable goods of the involved countries.

All this could lead to undervalued or overvalued currencies. So, is there a way to know if a currency is undervalued or overvalued?

## Real Exchange Rate

One way to determine whether a currency is undervalued or overvalued is by calculating the **Real Exchange Rate** (RER) **[3]**. This is the nominal exchange rate multiplied by the ratio of prices between the two countries. Those prices involve tradable and non-tradable goods. Let’s see this in more detail following the analysis of the paper **[2]**:

Considering the Law of One Price, we have that the price of a good is:

$$p_{i,t} = s_{t} + p_{i,t}^{*}$$

Where \(s_t\) is the log exchange rate, \(p_{i,t}\) is the log price of good * i* at time

*, and*

**t***denotes a foreign country variable.*

*****If we assume that the weights of each good are the same in the two implied countries, we can add up all the goods obtaining the following.

$$p_{t} = s_{t} + p_{t}^{*}$$

Considering that the basket of goods is composed of tradable and non-tradable goods, we can divide the previous equation as follows:

$$p_{t} = \alpha p_{N,t} + (1 – \alpha) p_{T,t}$$

Where \(\alpha\) is the percentage of non-tradable goods in the basket (denoted by N subscript), whereas \( (1 – \alpha) \) are the tradable goods (T subscript).

Therefore, the relative price level is:

$$r_{t} \equiv p_t – (p_{t}^{*} + s_{t}) = – (s_{t} – p_{t} +p_{t}^{*}) = – (s_{t} -p_{T,t} + p_{T,t}^{*}) + \alpha[p_{N,t} – p_{T,t}] – \alpha [p_{N,t}^{*} – p_{T,t}^{ *}] $$

Reorganizing the equation:

$$\omega \equiv [p_{N,t} – p_{T,t}] – [p_{N,t}^{*} – p_{T,t}^{*}]$$

We obtain the following:

$$r_{t} = r_{T,t} +\alpha \omega_{t}$$

By analyzing this expression, we can obtain two conclusion about how the variations in the real price level are produced:

- By changes in the relative price of
**traded goods**between countries. - By changes in the relative price of
**non-tradables**towards tradable goods in one country in relation to another.

## CPI bias

However, there may be a problem when it comes to measuring **CPI**s, since they could be affected by different measurement biases. As it is explained in the paper **[1]**, Sub-Saharan countries’ poverty reduction may be understated because of CPI bias.

Some of the most known types of bias are the following:

**Commodity substitution bias**. Quantities and weights are fixed in the base period and do not take into account the consumer’s behaviour towards cheaper goods.**Outlet substitution bias**. In some African countries, supermarkets that offer discounted prices are gaining popularity. CPI calculation does not consider these new trends and this leads to an overvalued inflation measure.**Quality change bias**. The quality of products evolve over the years and it is very difficult to know if the prices’ increase is due to this improve or it is due to inflation.**Bias from the introduction of new goods**. The introduction of new goods in the CPI calculation takes many years.

## Example

Let’s see an example of how **GDP calculation** is biased.

If we have a look at the ranking of countries ordered by nominal GDP, we can observe that the United States is in the top position of the ranking.

However, looking at the ranking ordered by GDP PPP, China is in the first position.

There is a fundamental discrepancy in the calculation of the two rankings.

The **nominal GDP** is calculated in each country’s currency and then the values are converted into dollars by using the value of the cross currency in order to set up the ranking. Whereas the **GDP PPP**, the PPP value is used, instead of the currency pair to convert each country’s GDP value into dollars.

Thus, we can confirm what has been said before, that the developed countries’ currencies are overvalued and those of developing countries undervalued. However, the GDP PPP value is also not completely **accurate** as it may suffer from the CPI bias problems which have been mentioned above.

## Conclusions

In this post, we have gone through what is the **Penn effect**, one of its consequences – which is the Harrod **Balassa Samuelson effect**– and the **bias** that **CPI** could have.

Depending on the way the GDP is calculated, we obtain different rankings. There is no better approach –each one has its pros and its cons. Therefore, to get an idea of the situation of each country, globally speaking, a good option would be to look at the different rankings and take into account the weaknesses of each one.

## References

**[1]** Dabalen, A., Gaddis, I., & Nguyen, N. T. V. (2020). CPI bias and its implications for poverty reduction in Africa. *The Journal of Economic Inequality*, *18*(1), 13-44.

**[2]** Cheung, Y. W., Chinn, M., & Nong, X. (2017). Estimating currency misalignment using the Penn effect: It is not as simple as it looks. *International Finance*, *20*(3), 222-242.

**[3]** https://www.imf.org/external/Pubs/FT/fandd/basics/42-real-exchange-rates.htm

**[4]** https://www.investopedia.com/terms/b/balassasamuelson-effect.asp

**[5]** https://www.econlib.org/cpi-bias-vs-the-penn-effect/

**[6]** https://en.wikipedia.org

**[7]** https://www.investopedia.com/